Critical Reynolds Number in an Oscillating Pipe Flow

A previous investigation revealed that, when turbulent bursts occur, the instantaneous velocity distribution and friction factor in an oscillating pipe flow are represented by the well-known 1/7 power law and by the turbulent quasi-steady values, respectively. Theses facts suggest that the mechanism of generating turbulence in an oscillating pipe flow is similar to that in a steady flow. Here an evaluation method of the critical Reynolds number is proposed by assuming that the generation region of turbulence is the same as that in a steady flow and by defining that the critical Reynolds number Reos, c is the value when the generation region is built up in a flow field. The estimated results agreed well with the experimental values. In addition, the relation between mean burst period T^-B in a steady turbulent pipe flow and critical frequency in an oscillating pipe flow at which turbulent bursts occur was obtained.